1. Field of the Invention
The present invention relates to an x-ray spectrum analysis system for spectra obtained with an electron microscope instrument. More particularly, the invention pertains to a computer based analyzer system which allows an analyst to extract quantitative information from experimentally acquired x-ray spectra and to simulate the experimental environment to generate theoretical spectra.
2. Description of Related Art
The physics and mathematics required to describe the generation and detection of a spectrum of characteristic and continuum x-rays resulting from the interaction of an electron beam with a specimen is described in an extensive body of literature. The generation of x-rays by interaction of an electron beam with a specimen is dependent upon the elemental composition of the specimen. Further complicating the process is the fact that detectors for the detection of x-rays have varying sensitivities, depending upon their construction. In use, the electron beam microscope is used to excite a spectrum representative of the sample. The final spectrum presented to the analyzer system depends on the specimen composition and geometry, the detector sensitivity, and the geometry of the electron microscope and detector configuration. The spectrum is then analyzed to determine the constituent elements of the sample and the relative proportions or absolute concentration of the elements in the sample.
The microprobe assay of a specimen must provide both a mean and the variance about this mean for each analyte or elemental constituent of a specimen. The mean refers to the estimate of the weight or atom concentration at a single analytical point, or some local grouping of points, from a homogeneous region of the specimen. The variance about this mean then represents the uncertainty due to counting statistics plus those aspects of the data reduction procedure which will contribute uncertainty, such as peak unraveling and continuum suppression. The accuracy of the estimate is a measure of the closeness of the estimate to the true value of the concentration. The task of predicting the variance about this estimated concentration can range from easy to quite difficult. As the specimen is further examined at many points, any variance greater than that determined above will represent true compositional variation. A significant period of time is required to collect enough data to analyze the specimen and estimate the concentration of the constituent elements to a sufficient accuracy and to a required level of confidence.
As with all measuring devices, the energy-dispersive x-ray analysis system has for a given set of conditions a sensitivity which translates into a minimum concentration of analyte that can be reported with a certain level of confidence. This quantity is often referred to as the minimum detectable limit (MDL) and its estimation can also range from easy to quite difficult.
A spectrum observed with an energy-dispersive spectrometer (EDS) consists of x-rays arising from both the characteristic and the continuum process. The x-ray peaks arising from the characteristic process contain the analytical information sought. Often the peaks to be determined overlap with the peaks from other elemental constituents of the specimen. Furthermore, the peaks are always superposed onto a smoothly varying spectrum of x-rays arising from the continuum process; and both the characteristic and continuum signals are modulated by the effects of counting statistics.
The MDL and variance about a measured concentration depend on the magnitude of the peak and background intensities, the degree of peak overlap, and the algorithms used to extract the required peak intensity and background intensity values below the peak. In general, there is no straightforward way of estimating the quantities required for standard statistical treatment. Therefore, many analysts, when faced with the problem of providing good error estimates, resort to the time-consuming but extremely reliable technique of direct measurement. In this method the specimen is sampled n times at a number of representative locations. For each of the n replicate measurements at each location one goes through all the spectra processing and data reduction steps required to arrive at an elemental concentration, where n is preferably greater than 25. From the n results at each location the analyst can then predict by conventional statistical methods the expected variance for each of the elemental concentrations at the various presumably representative locations. Knowing the expected variances the analyst can then proceed on with a strategy of single measurements at each analytical point in the specimen. For specimens with many phases or a wide range of compositions this procedure can be quite daunting. One approach to reducing the amount of time expended collecting the spectra data is to predict the minimum detectable limit achievable under proposed experimental conditions and to adjust these conditions to meet the requirements of the analysis.
There is an ever-growing body of knowledge concerning the physics of electron-specimen interaction and of the energy-dispersive x-ray spectrometer used to detect the resulting x-rays. The requisite knowledge is now at hand to generate from first principles an x-ray spectrum that is more than sufficiently close in all of the germane physical and statistical properties to represent an actual spectrum from a real specimen. From generated spectra one could then deduce accurate estimates of variance about mean compositional values and MDL of any analyzable stable element in any stable matrix. One might also accurately estimate the elemental composition of the specimen without the need to measure a set of calibration standards. Furthermore, one might adjust the experimental parameters to determine the optimum set that will produce the lowest MDL. One could do that relatively rapidly before even presenting a specimen to the electron beam.
By so determining the minimum detectable limits, the experiment could be designed so as to collect sufficient but not excessive spectrum data.
The electron microscope system is an expensive system to procure and operate. When analysis of the collected spectrum is performed using the computer analysis system that is part of the electron microscope system, the electron microscope system may not be used for the collection of x-ray spectra data. It would be beneficial to separate the analysis of spectra function from the collection of spectra function.